In the version of RSLinx that I have, I can't change the port settings, but Brewer described how to do it from inside RSLogix. That works once you're connected. I don't have an 1100 here, but I do have a 1400. In case the 1100 is similar enough, here's how to use the LCD on the 1400:
1) Press ESC until you're at the top menu
2) Scroll down "Advanced Set" and press OK
3) Scroll down to ENET Cfg and press OK
4) Scroll to IP Address and press OK
5) Next to "ENET Mode", use the up/down arrows to select "Static" and press OK
6) You can now set the IP address, subnet mask, and default gateway address manually
Have you gotten your work PC connected to it?

A laptop without an Ethernet port? That's...weird.
Anyway, I've used an older version of this:
https://www.amazon.com/Linksys-Ethernet-Chromebook-Ultrabook-USB3GIG/dp/B00LIW8TBG/ref=sr_1_3?ie=UTF8&qid=1550777715&sr=8-3&keywords=linksys+usb+ethernet
It worked great. Are you using a virtual machine? If so, it's much easier to connect the USB adapter to the VM and install its drivers there too.
You need your network adapter to be on the same subnet as the PLC. Since your personal PC connected, you know the IP address of the ML1100, and it's probably already set to static. Set the USB network adapter to manually configured and give it a different IP address in the same subnet and it should "just work".
Can you ping the PLC from your company PC?
If so, go into RSLinx and set up an Ethernet devices driver. Type in the PLC's address in the configuration dialog.

The UIC adapter is for connecting to a DH485 device, like the SLC5/03 or L40B fixed chassis processors.
The ML1100 supports Ethernet, so you shouldn't need anything more than a simple network patch cable. Your PC and the PLC will need to have different IP addresses that are on the same subnet.
If you can't use Ethernet, I think the ML1100 has a DF1 port that you can use your preferred USB-RS232 adapter and the DF1 driver in RSLinx.

Hmmmm....
I tried to open the project in WinCC Flexible 2008 but I can't, probably because I have SP3, not SP4. I then tried a migration to Portal v13 but it won't let me, saying that only projects saved in SP2, SP3, or SP5 can be migrated. Is there any way you can save your WinCC project in version SP3? Go to Project, then select "Save as version".

Hmmmm.....
It may be something specific to the Asia version, but we were able to migrate an SP3 project to Portal with no issues. We also have v13 and v14 both installed, so that may be the difference. Can you share your WinCC project? I'll give it a try here. I don't have the Asia version of the software, so I can't guarantee it won't break something unexpectedly.

If the RS232/USB adapter is connected to the VM using the "removable devices" menu, go to Device Manager and double-check which COM port number it was assigned. It may not be the same port number it got last time, especially if it's plugged into a different physical USB port.
But, from what you said, it's configured for an ASCII protocol that RSLinx can't use (if your research is right, I haven't confirmed that).
Are you still using that scale? If so, you're not going to get very far with setting the COMMS to default. Once you download the program back to the PLC to get online, the port will revert and you'll be dumped offline. Since you're using the COM port for a scale, and DH+ to an HMI, you won't be able to use a 5/05 since the 5/05 doesn't have a DH+ port. Your best bet right now is probably to connect to it via DH+, which won't be cheap. Actually, a better bet is to replace the 5/04 with a 5/05 and the HMI with one that supports Ethernet. That may not be in your budget, though.
We've had very bad results from the AB U2DHP modules. They are very expensive and just stop working without having been "abused". For systems where we must use DH+, we have a couple of Prosoft Ethernet to DH+ modules (AN-X2-AB-DHRIO). They're pricey, and need an external power supply, but they've been flawless.
We used to have a ControlLogix chassis on our computer cart with a 1756-ENBT module in one slot and a 1756-DHRIO in another. That worked well too but was a little cumbersome and would only be cost effective if you had those components lying around unused.
Our standby for aftermarket cables has been these guys:
https://www.plccable.com/allen-bradley-1784-u2dhp-alternative-usb-to-data-highway-plus-dh-anc-120e/
We haven't tried their DH+/USB system since we already have the Prosoft system working, but it is cheaper than the AB version, at least for us with our AB pricing.
The SLC 5/04 has a round mini-DIN port and the 3-pin phoenix connector on the front. Both are the same DH+ port, so you can get your gateway device connected at the same time as the HMI.

Also, are you using a virtual machine? If so, try connecting the USB-Serial adapter directly to the VM instead of the host. We've had trouble with the physical COM port of the host not translating predictably to the VM.

You can also get a "standard" programming cable for the MicroLogix with their custom mini-DIN type connector on one end an a 9-pin d-shell connector on the other. I think that's the 1761-CBL-PM02 cable. Then, get a programming port with the 9-pin d-shell connector. You can then use just a standard serial cable to connect to your PC.
Edited to add:
The AB cable tends to be expensive, but here's an aftermarket one:
https://www.plccable.com/allen-bradley-micrologix-cable-serial-1761-cbl-pm02-90-deg-end/
We've used their cables before with great results.

Looking at the wiring diagram in the user manual, the 1756-OF8 doesn't require an external power supply connection. The analog signals are generated within the module using power it gets from the backplane. See page 144 of this manual:
https://literature.rockwellautomation.com/idc/groups/literature/documents/um/1756-um009_-en-p.pdf

Have you gotten anything back from the machine builder? You really need the *.apa file for the HMI for this project but you should try to get their copy of the *.RSS file too so you get the documentation for future use.

As mentioned above, someone with time on their hands will need to trace out the code and figure it out a line at a time. I can't do it for you on company time or on the company laptop and I don't have the software to do it on my own.

I hate to say it, but without the source files you have your work cut out for you. Do you have pictures of what the screens were and what they displayed?
The best possible outcome is that whoever built the machine is still around and you can get the source files from them.

The file you uploaded from the PLC is what's running the process, but it's not documented so it's difficult to identify what's going on.
Does the HMI power up at all? If so, do you have the software to upload the runtime file from the HMI? You need Factory Talk View Studio for ME. If so, that would be a far better resource for replacing the HMI if it's a new enough software version to be decompiled and the OEM didn't password protect it.

Another option, if you can rearrange the data (or copy it into an array that can be rearranged), is the SRT instruction. You give it an array and it sorts in ascending order so the largest value will end up at the bottom of the array.

If you want a very accurate sample every x amount of time, you can also use a periodic task. For what you're describing, though, it sounds like it doesn't have to be super accurate, so you can just use a self-resetting timer
Your HMI would display SampleDest.

Apparently the safety controller thing is a known anomaly in v28, corrected in v29. Of course, that doesn't help you if you can't upload what's there. I don't know if the upload issue is fixed in v29 or not.

There is a tech note that talks about this, it requires TechConnect:
https://rockwellautomation.custhelp.com/app/answers/detail/a_id/878545/page/1
Basically, it can be caused by having an asterisk at the beginning of a tag comment or symbols anywhere in the project documentation (music notes, smiley faces, etc). Unfortunately, the suggested fixes have to be done while downloading to the PLC, not when uploading (fix the documentation or uncheck the "Download Project Documentation and Extended Properties" box under controller properties). You would need the latest ACD file. Do you have even an older ACD file for that PLC?
ETA: It also says NOT to uncheck that box if it's a safety controller using Add-On instructions. So be careful.

Ah, I see. I misread your reply too. I guess it also depends on why he reduced the update rate in the first place. To save network traffic or to just slow down how often the numbers change on the display? If it's just to reduce how often they change on the display, he could buffer them in the PLC, but if he wants to reduce network traffic, that won't help.